Find Zeros of Polynomial Function

Joined
Jun 27, 2021
Messages
5,386
Reaction score
422
Section 2.5
Question 56


20210919_211300.jpg


Can you do 56 as a guide for me to do the rest on my own?
 
56.

f(x)=2x^3+3x^2+18x+27

given zero: 3i -> so we will also have -3i

factors are (x-3i) and (x+3i)

their product is: (x-3i) (x+3i)=x^2-(3i)^2=x^2-9(-1)=x^2+9

use long division
..........(2x+3
x^2+9| 2x^3+3x^2+18x+27
..........2x^3+0*x^2+18x
......................3x^2+27
.........................3x^2+27
...................................0

last factor is 2x+3 and third zero is
2x+3=0
2x=-3
x=-3/2

so, zeros are: 3i, -3i, -3/2
 
56.

f(x)=2x^3+3x^2+18x+27

given zero: 3i -> so we will also have -3i

factors are (x-3i) and (x+3i)

their product is: (x-3i) (x+3i)=x^2-(3i)^2=x^2-9(-1)=x^2+9

use long division
..........(2x+3
x^2+9| 2x^3+3x^2+18x+27
..........2x^3+0*x^2+18x
......................3x^2+27
.........................3x^2+27
...................................0

last factor is 2x+3 and third zero is
2x+3=0
2x=-3
x=-3/2

so, zeros are: 3i, -3i, -3/2

In terms of long division, what term is the dividend and which one is the divisor?
 
The number that is being divided (in this case, 2x^3+3x^2+18x+27) is called the dividend,
and the number that it is being divided by (in this case, x^2+9) is called the divisor.
 
The number that is being divided (in this case, 2x^3+3x^2+18x+27) is called the dividend,
and the number that it is being divided by (in this case, x^2+9) is called the divisor.

I could not make out the difference between the dividend and divisor as typed in your first reply.
 

Members online

No members online now.

Trending content

Forum statistics

Threads
2,531
Messages
9,860
Members
697
Latest member
lemon in icewine
Back
Top